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Sinica-NCTS Geometry Seminar
16:00 - 17:00, May 17, 2019 (Friday)
Room 617, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 617室)
S^1-equivariant Index Theorems and Morse Inequalities on Complex Manifolds with Boundary
Guokuan Shao (Academia Sinica)


In this talk, we will present new versions of index theorems and Morse inequalities on complex manifolds with boundary. Let M be a relatively compact open subset with connected smooth boundary X in a complex manifold M'. Assume that M admits a holomorphic S1-action preserving the boundary X and the S1-action is transversal and CR on X. We claim that the m-th Fourier component of the q-th Dolbeault cohomology group is of finite dimension. By using Poisson operator, we prove a reduction theorem which shows that the formulas about in our main theorems involve only integrations over X. This talk is based on joint work with Chin-Yu HSIAO, Rung-Tzung HUANG and Xiaoshan LI.


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